Impacts of Priors on Convergence and Escapes from Nash Inflation

Thomas J. Sargent and Noah Williams
Working Paper 2003-14
October 2003

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Recent papers have analyzed how adaptive agents may converge to and escape from self-confirming equilibria. All of these papers have imputed to agents a particular prior about drifting coefficients. In the context of a model of monetary policy, this paper analyzes dynamics that govern both convergence and escape under a more general class of priors for the government. The authors characterize how the shape of the prior influences the dynamics in important ways. There are priors for which the E-stability condition is not enough to assure local convergence to a self-confirming equilibrium. Their analysis also tracks down the source of differences in the sustainability of Ramsey inflation encountered in the analyses of Sims (1988) and Chung (1990), on the one hand, and Cho, Williams, and Sargent (2002), on the other.

JEL classification: E3, D8, E5

Keywords: self-confirming equilibrium, mean dynamics, escape route, large deviation, natural rate of unemployment, adaptation, priors

We thank Jess Benhabib, Jim Bullard, Lars Peter Hansen, Seppo Honkapohja, and Tao Zha for helpful comments. Pierre-Olivier Weill provided research assistance. This paper was presented at the Monetary Policy and Learning Conference sponsored by the Federal Reserve Bank of Atlanta in March 2003. The views expressed here are the authors’ and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System. Any remaining errors are the authors’ responsibility.

Please address questions regarding content to Tom Sargent, Department of Economics, New York University, 269 Mercer Street, 8th Floor, New York, New York 10003, 212-998-3548,, or Noah Williams, Department of Economics, Princeton University, 308 Fisher Hall, Princeton, New Jersey 08544-1021, 609-258-4019,